Question 130730
let u="units digit", t="tens digit", and h="hundreds digit"


"the sum of the digits of a three digit number is 11" __ u+t+h=11


"If the digits are reversed, the new number is 46 more than five times the old number"
__ 100u+10t+h=5(100h+10t+u)+46 __ 100u+10t+h=500h+50t+5u+46


"the hundreds digit plus twice the tens digit is equal to the units digit"
__ h+2t=u


substituting __ (h+2t)+t+h=11 __ 3t+2h=11 __ 3t=11-2h __ multiplying by 50 __ 150t=550-100h


substituting __ 100(h+2t)+10t+h=500h+50t+5(h+2t)+46 __ 101h+210t=505h+60t+46
__ 150t=404h+46


substituting __ 550-100h=404h+46 __ 504=504h __ 1=h


substituting __ 3t+2(1)=11 __ 3t=9 __ t=3


substituting __ 1+3+u=11 __ u=7